Equation 8 · Part 3 · What a Rule Can Bind When the System Changes Weekly

Symbol C^*

C_{\mathrm{eq}}(t) = C^{*} \cdot 2^{\,t/\tau}, \qquad \tau \approx 8\ \mathrm{months}.

C^{*}

What this part means

$C^*$ is one factor in the product that computes the quantity on the left.

Its job in the formula

$C^*$ is one factor in the product that computes the quantity on the left.

Full expressionSymbol C^*Article meaning

The passage around this formula

…to 2023, estimated that the compute required to reach a set performance threshold has halved roughly every eight months, with a 95% confidence interval of about five to fourteen months [ 19 ] . If a threshold is fixed at $C^{*}$ and efficiency improves with a halving time $\tau$ , the capability reachable below the threshold grows as though the budget were expanding: $C_{\mathrm{eq}}(t) = C^{*} \cdot 2^{\,t/\tau}, \qquad \tau \approx 8\ \mathrm{months}$ . The analysis that follows is mine rather than the authors’. Taking the central estimate at face value, a threshold left unamended for…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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